Staff Selection Commission Combined Higher Secondary Level Exam
Question : The length of the chord of a circle is 8 cm and the perpendicular distance between the centre and the chord is 3 cm, then the diameter of the circle is equal to:
Option 1: 5 cm
Option 2: 10 cm
Option 3: 3 cm
Option 4: 7 cm
Correct Answer: 10 cm
Solution : Distance of perpendicular from centre to chord, $OD=3$ cm Length of chord, $AB=8$ cm We know that perpendicular from the centre to the chord bisects the chord. So, $AD=BD = 4$ cm Radius = $OB$ In $\Delta OBD$ $OB^2=BD^2+OD^2$ ⇒ $OB^2=4^2+3^2$ ⇒ $OB=5$ cm
Question : In a 5 km race, S gave a 500 m head start to T. If they finished the race at the same time and the speed of T is 13.5 km/hr, the speed of S is:
Option 1: 15 km/hr
Option 2: 20 km/hr
Option 3: 17.5 km/hr
Option 4: 16.5 km/hr
Correct Answer: 15 km/hr
Solution : Let the speed of S as \(v\) km/hr. Given that S gave a 500 m (or 0.5 km) head start to T, S has to run 5 km while T runs 4.5 km. Since they finish the race at the same time, their times
Question : A certain sum becomes 4 times of itself in 5 years at a rate of simple interest. In 15 years it will become how many times of itself at the same rate of simple interest?
Option 1: 12
Option 2: 10
Option 3: 9
Option 4: 8
Correct Answer: 10
Solution : Given, A sum becomes 4 times itself in 5 years Time = 15 years Let the principal be $P$. So, interest in 5 years $\small=4P - P = 3P$ We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$ ⇒ Rate $= \frac{3P\times100}{P\times5}=60$% In 15
Question : Directions: Select the option in which the numbers share the same relationship in the set as that shared by the numbers in the given set. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g.13 – operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) (8, 5, 39) (14, 11, 75)
Option 1: (12, 6, 70)
Option 2: (9, 5, 54)
Option 3: (11, 7, 74)
Option 4: (7, 4, 33)
Correct Answer: (7, 4, 33)
Solution : Given: (8, 5, 39); (14, 11, 75)
Add the first and the second number and multiply the resultant number by 3 to obtain the third number in the given set of numbers. ⇒ (8, 5, 39)→(8 + 5) × 3 = 13 ×
Question : Directions: From the given alternatives, select the word that can be formed using the letters of the given word. ENDEARMENT
Option 1: TENT
Option 2: TEMPER
Option 3: MEANS
Option 4: TENDER
Correct Answer: TENDER
Solution : Given: ENDEARMENT
Now, let's compare all the option words with the word ENDEARMENT – First option: TENT; The letter T appears only once in the word ENDEARMENT. But, in TENT, T appears two times. Therefore, all the letters of TENT are not present in the
Question : The Garba dance is performed in which state?
Option 1: Haryana
Option 2: Kerala
Option 3: Gujarat
Option 4: Punjab
Correct Answer: Gujarat
Solution : The correct answer is Gujarat.
Garba is a dance form that originated in Gujarat. The word garba refers to the social and religious event or gathering at which the dance is performed.
Question : Who among the following has been elected as the new President of the Board of Control for Cricket in India (BCCI) in October 2022?
Option 1: Roger Binny
Option 2: Sachin Tendulkar
Option 3: Kapil Dev
Option 4: Ravi Shastri
Correct Answer: Roger Binny
Solution : The correct answer is Roger Binny.
Former cricketer Roger Binny, who played a crucial role in India's 1983 World Cup victory, has assumed the role of President at the Board of Control for Cricket in India (BCCI). Taking over from former Indian cricket
Question : What is the volume of a cube whose side length is 6 metres?
Option 1: 36 cubic metres
Option 2: 120 cubic metres
Option 3: 208 cubic metres
Option 4: 216 cubic metres
Correct Answer: 216 cubic metres
Solution : Given: Side length = 6 m Volume of the cube = (side)3 = 63 = 216 cubic metres Hence, the correct answer is 216 cubic metres.
Question : 50% of A is equal to 80% of B. What is the ratio of A to B?
Option 1: 5 : 8
Option 2: 5 : 4
Option 3: 4 : 5
Option 4: 8 : 5
Correct Answer: 8 : 5
Solution : 50% of A is equal to 80% of B ⇒ $\frac{50}{100}\times{\text{A}} = \frac{80}{100}\times{\text{B}}$ ⇒ 5A = 8B ⇒ A : B = 8 : 5 Hence, the correct answer is 8 : 5.
Question : Directions: In the following question, select the one which is different from the other three alternatives.
Option 1: 187 : 11
Option 2: 194 : 12
Option 3: 195 : 13
Option 4: 224 : 14
Correct Answer: 194 : 12
Solution : Let's check the options – First option: 187 : 11; 187 ÷ 11 = 17; 187 is divisible by 11. Second option: 194 : 12; 194 ÷ 12 = 16.17; 194 is not divisible by 12. Third option: 195 : 13; 195 ÷
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